Structure of rings with certain conditions on zero divisors
Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R:x=a+b, where a is nilpotent, b is potent, and ab=ba. We call such a ring a D*-ring. We give the structure of periodic D*-ring, weakly periodic D*-ring, Artinian D*-ring, semiperfec...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/67692 |
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| _version_ | 1832555933158342656 |
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| author | Hazar Abu-Khuzam Adil Yaqub |
| author_facet | Hazar Abu-Khuzam Adil Yaqub |
| author_sort | Hazar Abu-Khuzam |
| collection | DOAJ |
| description | Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R:x=a+b, where a is nilpotent, b is potent, and ab=ba. We call such a ring a D*-ring. We give the structure of periodic D*-ring, weakly periodic D*-ring, Artinian D*-ring, semiperfect D*-ring, and other classes of D*-ring. |
| format | Article |
| id | doaj-art-93dbcd310b714fc9bbf38fa768ff31f0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-93dbcd310b714fc9bbf38fa768ff31f02025-02-03T05:46:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/6769267692Structure of rings with certain conditions on zero divisorsHazar Abu-Khuzam0Adil Yaqub1Department of Mathematics, American University of Beirut, Beirut 1107 2020, LebanonDepartment of Mathematics, University of California, Santa Barbara 93106-3080, CA, USALet R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R:x=a+b, where a is nilpotent, b is potent, and ab=ba. We call such a ring a D*-ring. We give the structure of periodic D*-ring, weakly periodic D*-ring, Artinian D*-ring, semiperfect D*-ring, and other classes of D*-ring.http://dx.doi.org/10.1155/IJMMS/2006/67692 |
| spellingShingle | Hazar Abu-Khuzam Adil Yaqub Structure of rings with certain conditions on zero divisors International Journal of Mathematics and Mathematical Sciences |
| title | Structure of rings with certain conditions on zero divisors |
| title_full | Structure of rings with certain conditions on zero divisors |
| title_fullStr | Structure of rings with certain conditions on zero divisors |
| title_full_unstemmed | Structure of rings with certain conditions on zero divisors |
| title_short | Structure of rings with certain conditions on zero divisors |
| title_sort | structure of rings with certain conditions on zero divisors |
| url | http://dx.doi.org/10.1155/IJMMS/2006/67692 |
| work_keys_str_mv | AT hazarabukhuzam structureofringswithcertainconditionsonzerodivisors AT adilyaqub structureofringswithcertainconditionsonzerodivisors |